Ground evaporation formula (Water Overlay): Difference between revisions

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Feddes oxygen stress factor:
Feddes oxygen stress factor:
<math>f_o =  
<math>f_o =
\begin{cases}
\begin{cases}
1.0 & \text{if } d_{gw,t} \text{ is } >= d_{r,3}} \\
1.0 & \text{if } d_{gw,t} \text{ is } \geq d_{r,3} \\
\frac{d_{gw,t} -  d_{r,4}}{d_{r,3} -  d_{r,4}} & \text{if } d_{gw,t} \text{ is } >= d_{r,4}} \\
\frac{d_{gw,t} -  d_{r,4}}{d_{r,3} -  d_{r,4}} & \text{if } d_{gw,t} \text{ is } \geq d_{r,4} \\
0.0 & \text{otherwise} \\
0.0 & \text{otherwise}
\end{cases}
\end{cases}
</math>
</math>
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<math>f_s =  
<math>f_s =  
\begin{cases}
\begin{cases}
0.0 & \text{if } d_{gw,t} \text{ is } >= d_{r,1}} \\
0.0 & \text{if } d_{gw,t} \text{ is } >= d_{r,1} \\
1.0 - \frac{d_{gw,t} -  d_{r,2}}{d_{r,1} -  d_{r,2}} & \text{if } d_{gw,t} \text{ is } >= d_{r,2}} \\
1.0 - \frac{d_{gw,t} -  d_{r,2}}{d_{r,1} -  d_{r,2}} & \text{if } d_{gw,t} \text{ is } >= d_{r,2} \\
1.0 & \text{otherwise} \\
1.0 & \text{otherwise}
\end{cases}
\end{cases}
</math>
</math>
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Evaporation saturated:
Evaporation saturated:
<math>h_{s} = w_{g,t} - ( b_{s} - d_{gb} )</math>
<math>h_{s} = w_{g,t} - ( b_{s} - d_{gb} )</math>
<math>h_{r} = max( 0.0 ,  w_{g,t} - ( b_{s} - d_{r,1} ))</math>
<math>h_{r} = max( 0.0 ,  w_{g,t} - ( b_{s} - d_{r,1} ))</math>
<math>E_{sp} = (E_{max} - E_{u}) \cdot f_s</math>
<math>E_{sp} = (E_{max} - E_{u}) \cdot f_s</math>
<math>E_{s} = max (0.0 , min ( E_{sp}, h_{s}\cdot f_{gw}, h_r \cdot f_{gw}</math>
<math>E_{s} = max (0.0 , min ( E_{sp}, h_{s}\cdot f_{gw}, h_r \cdot f_{gw}</math>


Revision as of 13:02, 25 February 2021

Underground evaporation is calculated per cell.

For all underground evaporation calculation, the ground water depth at time t is used. Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle d_{gw,t} = b_{s} - w_{g,t}}

Feddes oxygen stress factor: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f_o = \begin{cases} 1.0 & \text{if } d_{gw,t} \text{ is } \geq d_{r,3} \\ \frac{d_{gw,t} - d_{r,4}}{d_{r,3} - d_{r,4}} & \text{if } d_{gw,t} \text{ is } \geq d_{r,4} \\ 0.0 & \text{otherwise} \end{cases} }

Feddes saturated zone root update factor: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f_s = \begin{cases} 0.0 & \text{if } d_{gw,t} \text{ is } >= d_{r,1} \\ 1.0 - \frac{d_{gw,t} - d_{r,2}}{d_{r,1} - d_{r,2}} & \text{if } d_{gw,t} \text{ is } >= d_{r,2} \\ 1.0 & \text{otherwise} \end{cases} }

Max potential evaporation:

Evaporation unsaturated: Failed to parse (unknown function "\begin{cases}"): {\displaystyle E_{u} = \begin{cases} 0.0 & \text{if } d_{us} \text{ is } <= 0.0} \\ min(E_{max}, h_u \cdot \frac{d_{r,1}}{d_{gw,t}})& \text{otherwise} \\ \end{cases} }

Evaporation saturated:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle h_{r} = max( 0.0 , w_{g,t} - ( b_{s} - d_{r,1} ))}

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle E_{sp} = (E_{max} - E_{u}) \cdot f_s}

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle E_{s} = max (0.0 , min ( E_{sp}, h_{s}\cdot f_{gw}, h_r \cdot f_{gw}}

Evaporation total is the sum of evaporation in the saturated and unsaturated zone: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle E = E_u + E_s}

where

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle b_{s}} is the datum height of the surface.
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle w_{g}} is the underground water level.
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle d} is the column height of the unsaturated zone.
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f_t} is the transpiration factor of the buildings (plants) on the surface, or the surface terrain's

[Terrain_water_evaporation_factor_(Water_Overlay)|transpiration factor]] if none present.

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle E_{w,t}} is the evaporation rate of the weather at time t
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f_0} is the feddes oxygen stress factor, calculated using the 3rd and 4th root depths and the feddes trapezium interpolation model and the ground water depth.


Related

The following topics are related to this formula.

Formulas
Groundwater level formula
Models
Underground model
Evaporation model
Water Module
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Water Module
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Tutorials
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Overview
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Theory
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Benchmarks
Models
Surface • Ground • Rain • Evaporation • Infiltration • Elevation • Breach • Sewer • Storage • Tracer flow • Border • Order
Model formulas
Timestep • Season • Surface water level • Groundwater level
Flow formulas
Surface flow • Surface infiltration • Ground flow • Ground infiltration • Surface evaporation • Ground evaporation • Ground bottom flow
Hydraulic structure formulas
Culvert • Weir • Breach growth • Breach flow • Pump • Sewer Overflow • Inlet • Drainage
Related
Building attributes • Hydrological features • Hydraulic structures •  Terrain attributes • Model attributes • Results • Simulation data
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